Morphometric distribution of depth and basin shape in Aotearoa New Zealand lakes

Using machine learning to improve national lake depth predictions

Tadhg Moore, Chris McBride, Deniz Özkundakci, Mathew Allen, Moritz K Lehmann, Matthew J Prentice, Whitney Woelmer, Maggie Armstrong, Kevin Rose

2024-11-19

Motivation

Developing the Lake Ecosystem Research New Zealand modelling platfom (LERNZmp).
Lake depth and morphometry are key drivers of lake ecosystem function, therefore accurate depth data is essential (Ganz, Glines, and Rose 2024).
The Freshwater Ecosystems New Zealand (FENZ) database is the most comprehensive database of lake morphometry in New Zealand, but is limited in its depth data.
NZ lakes provide a unique opportunity to develop a comprehensive database of lake depth and morphometry, particularly given the diversity of lake size, depth and geomorphic type.

Objectives

Develop a comprehensive database of lake depth and morphometry for New Zealand.
Use machine learning to predict mean and maximum lake depth from this data.
Compare these predictions to the FENZ database and other global lake depth databases e.g. maximum lake depths - GLOBathy(Khazaei et al. 2022) and mean lake depth - HydroLAKES (Messager et al. 2016)

FENZ Lakes

Lack of a central database on lake morphometry, particularly depth
Large number of bathymetric data has been recorded across lakes in New Zealand
Current predictions of max lake depth, within the FENZ database (n=3475) are limited and have clear biases

Figure 1: Depth distribution of FENZ lakes. The x-axis is log10 scaled.

Methods

Bathymetry survey data were sourced from a variety of sources - paper maps, digital files, and online databases (n=156).

Lake maximum depth data which were known, but did not have bathymetry data available were added to the dataset (n=36) bringing us to a total of 192 lakes with maximum depth data.

Shoreline data were updated using satellite and aerial imagery.

Depth data were interpolated using a Multilevel B-Spline Approximation (MBA) algorithm.

Hypsographic curves were calculated for each lake.

Comparison of depth and area with other databases.

Used machine learning to predict lake depth from morphometric data for all lakes in New Zealand and benchmark against the FENZ dataset.

Bathymetry example: Lake Rotoma

Depth contours

Figure 2: Depth contours of Lake Rotoma, a large lake in the Bay of Plenty region.

Bathymetry example: Lake Rotoma

Bathymetry raster

Figure 3: Depth raster of Lake Rotoma, a large lake in the Bay of Plenty region.

Bathymetry example: Lake Rotoma

Estimated lake bed

Figure 4: Three dimensional rendering of Lake Rotoma’s bathymetry.

Bathymetry example: Lake Rotoma

Estimated hypsographic curve

Figure 5: Hypsograph curve of Lake Rotoma.

Hypsographic summary

Table 1: Hypsographic summary of Lake Rotoma

Variable	Value
Max depth	90.40
Mean depth	45.33
Volume development index	1.50
Area (ha)	1063.51
Shoreline length (km)	23.40
Shoreline development index	2.04

Lakes with bathymetry data

Lakes with bathymetric data are relatively evenly distributed across New Zealand.
Lake geomorphic type is highly regionalised.
Lakes which have maximum depth data but no bathymetry data highlight that there is probably a further bathymetry data out there.
Some lakes, particularly glacial lakes might have quite a dynamic bathymetry.

Depth-area relationship

Figure 7: Summary of measured lake area and max depth by latitude and elevation (n=192). The size of the point represents the elevation of the lake.

Breakdown by geomorphic type

Figure 8: Summary of measured lake area and max depth by geomorphic type.

Distribution of lake hypsograph shape

Figure 9: Distribution of hypsograph shape by geomorphic type. Solid black line indicated the median and the dashed red line represents the 1:1 line.

Distribution of volume development

Development of Volume, \(D_V\) (Hutchinson 1957) is a measure of departure of the shape of the lake basin from that of a cone calculated using the maximum depth \(Z_{max}\) and the average depth \(\bar{Z}\) :

\[D_V = \frac{3 \times \bar{Z}}{Z_{max}}\] \(D_V\) is greatest in shallow lakes with flat bottoms and low in deep lakes with steep sides.

Figure 10: Distribution of volume development (DV) by geomorphic type.

Used a random forest machine learning model from the caret R package to predict mean and maximum lake depth from morphometric data (Kuhn 2008).
Covariates included variables available for all lakes in the dataset: lake area, elevation, latitude, shoreline development index, geomorphic type and other climate and catchment characteristics.

Figure 11: Predicted vs observed max depth. Note that the x and y axes are log10 scaled.

Table 2: Model fit for max depth

Source	N	Bias	RMSE	R2
FENZ	183	-0.79	44.64	0.70
GloBATHY	119	20.93	72.68	0.43
ML model	190	-0.49	19.17	0.95

Figure 12: Predicted vs observed mean depth. Note that the x and y axes are log10 scaled.

Figure 13: Predicted vs observed mean depth. Note that the x and y axes are log10 scaled.

Table 3: Model fit for mean depth

Source	N	Bias	RMSE	R2
FENZ	155	6.24	21.59	0.71
Hydrolakes	91	7.27	22.48	0.79
ML model	155	-0.15	7.80	0.97

Conclusions

Bathymetric data from 156 lakes were digitised and collated for use in this study.
Using a machine learning model, we were able to predict maximum lake depth from morphometric data with an \(r^2\) = 0.95 and mean lake depth with an \(r^2\) = 0.97.
This was substantially better than the FENZ dataset, which had an \(r^2\) = 0.7 for max depth and 0.71 for mean depth.

Applications

All data is available within the LERNZmp.
For lakes without bathymetric data, we can predict lake depth with a high degree of accuracy compared to other datasets.
Highlights lakes with limited depth data to target for future surveying.
Provides a comprehensive database of lake depth, morphometry and other characteristics within Aotearoa New Zealand for future research.

Acknowledgements

This project was funded by the New Zealand Ministry of Business, Innovation and Employment (MBIE) through the Smart Ideas program within the Endeavour Fund (grant UOWX2103).
We would like to thank all our data contributors who provided data for the LERNZmp project.

References

Ganz, Keenan J., Max R. Glines, and Kevin C. Rose. 2024. “The Distribution of Depth, Volume, and Basin Shape for Lakes in the Conterminous United States.” Limnology and Oceanography 69 (1): 22–36. https://doi.org/10.1002/lno.12475.

Khazaei, Bahram, Laura K. Read, Matthew Casali, Kevin M. Sampson, and David N. Yates. 2022. “GLOBathy, the Global Lakes Bathymetry Dataset.” Scientific Data 9 (1): 36. https://doi.org/10.1038/s41597-022-01132-9.

Kuhn, Max. 2008. “Building Predictive Models in R Using the Caret Package.” Journal of Statistical Software 28 (November): 1–26. https://doi.org/10.18637/jss.v028.i05.

Messager, Mathis Loïc, Bernhard Lehner, Günther Grill, Irena Nedeva, and Oliver Schmitt. 2016. “Estimating the Volume and Age of Water Stored in Global Lakes Using a Geo-Statistical Approach.” Nature Communications 7 (1): 13603. https://doi.org/10.1038/ncomms13603.